2.) Generally crab apple are considered better pollinates for apple trees then actual apples. The apples we grow are essentially clones of freak mutant crab apples that put way more energy into making big fruit then their wild ancestors, often at the expense of other things. Many produce negligible amounts of pollen.
3.) No. The fruit is essentially like the womb or uterus...it's a part of the parent tree. If you plant the seeds they might grow into trees with fruit that take qualities from the "father"...but apple tree heredity is unpredictable.

Thank you Ed. Is 'any' crab apple tree ok, or would certain types serve my purpose better?

PS - "freak mutant clones" made me chuckle

1. Minimally self-fertile, if at all. You'll want to get another cultivar to ensure pollination.

2. There's no single "best partner". You can Google 'Honeycrisp pollination' and get many, many, many options. If you have crabapples nearby, you could possibly even depend on them to provide the service.

3. Nope. It doesn't work that way!